What is 3log_{2}(x)-4log_{2}(x+3)-2log_{2}(y) ?

The solution to 3log_{2}(x)-4log_{2}(x+3)-2log_{2}(y) is log_{2}((x^3)/((x+3)^4y^2))

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simplify 3log_{2}(x)-4log_{2}(x+3)-2log_{2}(y)

simplify

3 lo g_{2} (x) - 4 lo g_{2} (x + 3) - 2 lo g_{2} (y)

lo g_{2} (\frac{x ^{3}}{( x + 3 ) ^{4} y ^{2}})

Solution steps

3 lo g_{2} (x) - 4 lo g_{2} (x + 3) - 2 lo g_{2} (y)

3 lo g_{2} (x) = lo g_{2} (x^{3})

- 4 lo g_{2} (x + 3) = - lo g_{2} ((x + 3)^{4})

- 2 lo g_{2} (y) = - lo g_{2} (y^{2})

= lo g_{2} (x^{3}) - lo g_{2} ((x + 3)^{4}) - lo g_{2} (y^{2})

Apply log rule:

lo g_{a} (x) - lo g_{a} (y) = lo g_{a} (\frac{x}{y})

lo g_{2} (x^{3}) - lo g_{2} ((x + 3)^{4}) = lo g_{2} (\frac{x ^{3}}{( x + 3 ) ^{4}})

= lo g_{2} (\frac{x ^{3}}{( x + 3 ) ^{4}}) - lo g_{2} (y^{2})

Apply log rule:

lo g_{a} (x) - lo g_{a} (y) = lo g_{a} (\frac{x}{y})

lo g_{2} (\frac{x ^{3}}{( x + 3 ) ^{4}}) - lo g_{2} (y^{2}) = lo g_{2} \frac{\frac{x ^{3}}{( x + 3 ) ^{4}}}{y ^{2}}

= lo g_{2} \frac{\frac{x ^{3}}{( x + 3 ) ^{4}}}{y ^{2}}

Simplify

\frac{\frac{x ^{3}}{( x + 3 ) ^{4}}}{y ^{2}} : \frac{x ^{3}}{( x + 3 ) ^{4} y ^{2}}

= lo g_{2} (\frac{x ^{3}}{( x + 3 ) ^{4} y ^{2}})

lo g_{10} (\frac{x ^{4} z ^{3}}{y})

lo g_{3} (27 x^{4})

lo g_{10} (1) + lo g_{10} (2) + lo g_{10} (3)

lo g_{10} (2.3) - lo g_{10} (3.1)

lo g_{4} (x) + lo g_{4} (x - 3)

What is 3log_{2}(x)-4log_{2}(x+3)-2log_{2}(y) ?
The solution to 3log_{2}(x)-4log_{2}(x+3)-2log_{2}(y) is log_{2}((x^3)/((x+3)^4y^2))